122,273 research outputs found
Adiabatic quantum computing with parameterized quantum circuits
Adiabatic quantum computing is a universal model for quantum computing.
Standard error correction methods require overhead that makes their application
prohibitive for near-term devices. To mitigate the limitations of near-term
devices, a number of hybrid approaches have been pursued in which a
parameterized quantum circuit prepares and measures quantum states and a
classical optimization algorithm minimizes an objective function that
encompasses the solution to the problem of interest. In this work, we propose a
different approach starting by analyzing how a small perturbation of a
Hamiltonian affects the parameters that minimize the energy within a family of
parameterized quantum states. We derive a set of equations that allow us to
compute the new minimum by solving a constrained linear system of equations
that is obtained from measuring a series of observables on the unperturbed
system. We then propose a discrete version of adiabatic quantum computing which
can be implemented with NISQ devices while at the same time is insensitive to
the initialization of the parameters and to other limitations hindered in the
optimization part of variational quantum algorithms. We also derive a lower
bound on the number of discrete steps needed to guarantee success. We compare
our proposed algorithm with the Variational Quantum Eigensolver on two
classical optimization problems, namely MaxCut and Number Partitioning, and on
a quantum-spin configuration problem, the Transverse-Field Ising Chain model,
and confirm that our approach demonstrates superior performance.Comment: 22 pages, 8 figures; v2 minor correction
Collective Coordinate Control of Density Distributions
Real collective density variables [c.f.
Eq.\ref{Equation3})] in many-particle systems arise from non-linear
transformations of particle positions, and determine the structure factor
, where denotes the wave vector. Our objective is to
prescribe and then to find many-particle configurations
that correspond to such a target using a numerical optimization
technique. Numerical results reported here extend earlier one- and
two-dimensional studies to include three dimensions. In addition, they
demonstrate the capacity to control in the neighborhood of
0. The optimization method employed generates
multi-particle configurations for which , , and 1, 2, 4,
6, 8, and 10. The case 1 is relevant for the Harrison-Zeldovich
model of the early universe, for superfluid , and for jammed
amorphous sphere packings. The analysis also provides specific examples of
interaction potentials whose classical ground state are configurationally
degenerate and disordered.Comment: 26 pages, 8 figure
Application of pattern search method to power system valve-point economic load dispatch
Direct search (DS) methods are evolutionary algorithms used to solve constrained optimization problems. DS methods do not require any information about the gradient of the objective function at hand, while searching for an optimum solution. One of such methods is pattern search (PS) algorithm. This study presents a new approach based on a constrained pattern search algorithm to solve well-known power system economic load dispatch problem (ELD) with valve-point effect. For illustrative purposes, the proposed PS technique has been applied to various test systems to validate its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method has been assessed and investigated through comparison with results reported in literature. The outcome is very encouraging and proves that pattern search (PS) is very applicable for solving power system economic load dispatch problem
Classical Optimizers for Noisy Intermediate-Scale Quantum Devices
We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They are also used for calibration tasks, hyperparameter tuning, in machine learning, etc. We analyze the efficiency and effectiveness of different optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date concentrated on tuning the quantum VQE circuit, we show that, in the presence of quantum noise, the classical minimizer step needs to be carefully chosen to obtain correct results. We explore state-of-the-art gradient-free optimizers capable of handling noisy, black-box, cost functions and stress-test them using a quantum circuit simulation environment with noise injection capabilities on individual gates. Our results indicate that specifically tuned optimizers are crucial to obtaining valid science results on NISQ hardware, and will likely remain necessary even for future fault tolerant circuits
A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems
This study presents a new approach based on a hybrid algorithm consisting of Genetic Algorithm (GA), Pattern Search (PS) and Sequential Quadratic Programming (SQP) techniques to solve the well-known power system Economic dispatch problem (ED). GA is the main optimizer of the algorithm, whereas PS and SQP are used to fine tune the results of GA to increase confidence in the solution. For illustrative purposes, the algorithm has been applied to various test systems to assess its effectiveness. Furthermore, convergence characteristics and robustness of the proposed method have been explored through comparison with results reported in literature. The outcome is very encouraging and suggests that the hybrid GA–PS–SQP algorithm is very efficient in solving power system economic dispatch problem
A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry
We present here a review of the fundamental topics of Hartree-Fock theory in
Quantum Chemistry. From the molecular Hamiltonian, using and discussing the
Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock
equations for the electronic problem. Special emphasis is placed in the most
relevant mathematical aspects of the theoretical derivation of the final
equations, as well as in the results regarding the existence and uniqueness of
their solutions. All Hartree-Fock versions with different spin restrictions are
systematically extracted from the general case, thus providing a unifying
framework. Then, the discretization of the one-electron orbitals space is
reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition
of the basic underlying concepts related to the construction and selection of
Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we
close the review with a section in which the most relevant modern developments
(specially those related to the design of linear-scaling methods) are commented
and linked to the issues discussed. The whole work is intentionally
introductory and rather self-contained, so that it may be useful for non
experts that aim to use quantum chemical methods in interdisciplinary
applications. Moreover, much material that is found scattered in the literature
has been put together here to facilitate comprehension and to serve as a handy
reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and
subeqn package
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